Anomalous Quantum Mumbers and Topological Properties of Field Theories

• Main Author: Polychronakos, Alexios P.
• Format: Others
• Published: 1987
• Online Access: https://thesis.library.caltech.edu/7421/1/Polychronakos%201987.pdf; Polychronakos, Alexios P. (1987) Anomalous Quantum Mumbers and Topological Properties of Field Theories. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/PBQR-B016. https://resolver.caltech.edu/CaltechTHESIS:01222013-133723975 <https://resolver.caltech.edu/CaltechTHESIS:01222013-133723975>

<p>We examine the connection between anomalous quantum numbers, symmetry breaking patterns and topological properties of some field theories. The main results are the following: In three dimensions the vacuum in the presence of abelian magnetic field configurations behaves like a superconductor. Its quantum numbers are exactly calculable and are connected with the Atiyah-Patodi-Singer index theorem. Boundary conditions, however, play a nontrivial role in this case. Local conditions were found to be physically preferable than the usual global ones. Due to topological reasons, only theories for which the gauge invariant photon mass in three dimensions obeys a quantization condition can support states of nonzero magnetic flux. For similar reasons, this mass induces anomalous angular momentum quantum numbers to the states of the theory. Parity invariance and global flavor symmetry were shown to be incompatible in such theories. In the presence of massless flavored fermions, parity will always break for an odd number of fermion flavors, while for even fermion flavors it may not break but only at the expense of maximally breaking the flavor symmetry. Finally, a connection between these theories and the quantum Hall effectwas indicated.</p>